4,655 research outputs found
Local stability and a renormalized Newton Method for equilibrium liquid crystal director modeling
We consider the nonlinear systems of equations that result from discretizations of a prototype variational model for the equilibrium director field characterizing the orientational properties of a liquid crystal material. In the presence of pointwise unit-vector constraints and coupled electric fields, the numerical solution of such equations by Lagrange-Newton methods leads to problems with a double saddle-point form, for which we have previously proposed a preconditioned nullspace method as an effective solver [A. Ramage and E. C. Gartland, Jr., submitted]. The characterization of local stability of solutions is complicated by the double saddle-point structure, and here we develop efficiently computable criteria in terms of minimum eigenvalues of certain projected Schur complements. We also propose a modified outer iteration (“Renormalized Newton Method”) in which the orientation variables are normalized onto the constraint manifold at each iterative step. This scheme takes advantage of the special structure of these problems, and we prove that it is locally quadratically convergent. The Renormalized Newton Method bears some resemblance to the Truncated Newton Method of computational micromagnetics, and we compare and contrast the two
Phase Equilibrium and Optimization Tools: Application for Enhanced Structured Lipids for Foods
Solid-liquid phase equilibrium modeling of triacylglycerols mixtures is essential for lipids design. Considering the α polymorphism and liquid phase as ideal, the Margules 2-suffix excess Gibbs energy model with predictive binary parameter correlations describes the non ideal β and β’ solid polymorphs. Solving by direct optimization of the Gibbs free energy enables to predict from a bulk mixture composition the phases composition at a given temperature and thus the SFC curve, the melting profile and the Differential Scanning Calorimetry (DSC) curve that are related to end-user lipid properties. Phase diagram, SFC and DSC curve experimental data are qualitatively and quantitatively well predicted for the binary mixture 1,3-dipalmitoyl-2-oleoyl-sn-glycerol (POP) and 1,2,3-tripalmitoyl-sn-glycerol (PPP), the ternary mixture 1,3-dimyristoyl-2-palmitoyl-sn-glycerol (MPM), 1,2-distearoyl-3-oleoyl-sn-glycerol (SSO) and 1,2,3-trioleoyl-sn-glycerol (OOO), for palm oil and cocoa butter. Then, addition to palm oil of Medium-Long-Medium type structured lipids is evaluated, using caprylic acid as medium chain and long chain fatty acids (EPA-eicosapentaenoic acid, DHA-docosahexaenoic acid, γ-linolenic-octadecatrienoic acid and AA-arachidonic acid), as sn-2 substitutes. EPA, DHA and AA increase the melting range on both the fusion and crystallization side. γ-linolenic shifts the melting range upwards. This predictive tool is useful for the pre-screening of lipids matching desired properties set a priori
Structural, elastic and thermal properties of cementite (FeC) calculated using Modified Embedded Atom Method
Structural, elastic and thermal properties of cementite (FeC) were
studied using a Modified Embedded Atom Method (MEAM) potential for iron-carbon
(Fe-C) alloys. Previously developed Fe and C single element potentials were
used to develop an Fe-C alloy MEAM potential, using a statistically-based
optimization scheme to reproduce structural and elastic properties of
cementite, the interstitial energies of C in bcc Fe as well as heat of
formation of Fe-C alloys in L and B structures. The stability of
cementite was investigated by molecular dynamics simulations at high
temperatures. The nine single crystal elastic constants for cementite were
obtained by computing total energies for strained cells. Polycrystalline
elastic moduli for cementite were calculated from the single crystal elastic
constants of cementite. The formation energies of (001), (010), and (100)
surfaces of cementite were also calculated. The melting temperature and the
variation of specific heat and volume with respect to temperature were
investigated by performing a two-phase (solid/liquid) molecular dynamics
simulation of cementite. The predictions of the potential are in good agreement
with first-principles calculations and experiments.Comment: 12 pages, 9 figure
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